1 Answer
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This setting backs your data up to Google's magic cloud. It includes what apps you have installed, and some apps' settings (if they are written to take advantage of it) which are restored when you first sign in to a new phone.

You can choose to back up some of your
data, such as your bookmarks, your
user dictionary, your Wi-Fi passwords,
and many other settings, to your
Google Account, on Google servers.
Some third-party applications may also
take advantage of this feature. That
way, when you need to replace your
phone (when you upgrade or replace a
lost phone), or if you reinstall an
application, you can restore your
settings and other data. For
information about changing this
setting later, see “Privacy settings”
on page 370.

That setting controls apps' ability to use this API, which includes Google's apps such as Market.